A population proportion is to be estimated. Estimate the minimum sample size needed to achieve the specified margin of error with a 95% degree of confidence.
-$E = 0.04$
A)625
B)313
C)1250
D)25

Question

Quizplus · Accepted Answer

The minimum sample size needed to achieve a specified margin of error $E$ with a 95% confidence level, when the population proportion is unknown, can be estimated using the formula $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$. Assuming a worst-case scenario for maximum variance (i.e., $p = 0.5$), and using $Z = 1.96$ for a 95% confidence level, the calculation is $n = \frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.04^2} = 600.25$. Rounding up to the nearest whole number gives 601, but since 601 is not an option and 625 is the closest higher option provided, it is the correct choice for ensuring at least a 0.04 margin of error with 95% confidence.

A Population Proportion Is to Be Estimated E=0.04E = 0.04E=0.04 A)625 B)313 C)1250 D)25

A Population Proportion Is to Be Estimated $E = 0.04$ A)625
B)313
C)1250
D)25